Elementary students know square numbers. However, some square number related competition problems are not easy to solve (you can try these practice problems). This tutorial reveals some important properties of square numbers and discuss how to use these simple facts to solve real problems.

These properties are intuitive and do not require any advanced knowledge to understand. Many of them are related to remainders. The concept of remainder itself is not complicated, but for the sake of convenience and concise, we use MOD expression to describe remainders. Therefore, students should have some basic MOD knowledge. So they can understand that $a\equiv 1\pmod{4}$ means $a$ is divided by $4$, the remainder is $1$.